The quality of being worthy of intense dislike, hatred, or strong disapproval.
From 'detestable' (worthy of hatred) plus the noun suffix '-ity,' from Latin 'detestari' (to curse or abhor), combining 'de-' (away/down) and 'testari' (to witness).
The Latin root 'testari' originally meant to bear witness—so detestability literally means something is so bad it makes you want to testify AGAINST it!
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